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Individuals with bodily distress syndrome (hereafter BDS) experience daily bothersome physical symptoms. Typical symptoms are headache, pains in the back, muscles or joints, stomach trouble, breathlessness, excessive fatigue and many more.

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Amāvásyā (Sanskrit: अमावस्या) is the lunar phase of the new moon in Sanskrit. Indian calendars use 30 lunar phases, called tithi in India.[1][2] The dark moon tithi is when the Moon is within 12 degrees of the angular distance between the Sun and Moon before conjunction (syzygy).[3] The New Moon tithi (called Pratipada or Prathama) is the 12 angular degrees after syzygy. Amāvásyā is often translated as new moon since there is no standard term for the Moon before conjunction in English.

In Sanskrit, "amā" means "together" and "vásya" means "to dwell" or "cohabit". It also means "na" +"ma"+"asya" meaning to "na" = "No, "ma"=Moon, "Asya"="There" in turn meaning to There is no Moon i.e., Moon is not visible.

In the pūrṇimānta māna Hindu lunar calendar used in most parts of the Indian subcontinent, the lunar month starts on the day following the full moon or purnima and therefore Amāvásyā always falls in the middle of the month. However, in the amānta māna calendar used in some places, the lunar month starts on the day of the new moon, making Amāvásyā the last day of the lunar month in those places. Many festivals, the most famous being Diwali (the festival of lights), are observed on Amāvásyā. Many Hindus fast on Amāvásyā.

Few Pancha-Gauda Brahmins have month from next day of Purnima (day) to Purnima (day), that is Purnima is last 29/30 days (Purnimanta). Pancha-Dravida have month from next day of Amavasya to Amavasya . Amavasya is last 29/30 days (Amanta)[1]. Śhukla paksha is called as the bright half as the Moon changes from New Moon to Full Moon while in Krishna paksha it changes from Full Moon to New Moon. Hence it is seen that same Amavasya has same festival all over the country. Ujjain, Allahabad, Orissa, Bihar Brahmins are one few Pancha-Gauda Brahmins have month from 1 day after Purnima (day) to Purnima (day)(Purnimanta), While the people of Karnataka, Maharashtra, Goa, Gujarat, Kerala and Andhra Pradesh the Pancha-Dravida have month from 1 day after Amavasya to Amavasya. Amavasya is last 29/30 days (Amanta). Since Kanchipuram Mutt where the Adi Shankara lived and all the Pancha-Gauda and Pancha-Dravida use to visit hence Tamil Nadu developed a mixture of Panchangam and saka calendar. Similarly the place where Pancha-Gauda and Pancha-Dravida are living together as Rajasthan, Madhya Pradesh, Southern Uttar Pradesh and Chhattisgarh also show the mixtures. Also the people following Jainism follow Pancha-Dravida calendar, Amavasya is last 29/30 days.[2][clarification needed]

In old Indian culture and beliefs, irrespective of religions, Amavasya is considered a time of great power. In Tamil, though Amavasai is commonly used in religious spheres, the pure Tamil scholars prefer the term Puthuppi Rai[4] Fast is observed to propitiate both the Sun and Moon Gods.[5]

An Amavasya falling on Mondays has a special significance. It is believed that a fast on this particular Amavasya would ward off widow-hood in women and ensure bearing of progeny. It is also believed that all desires could be fulfilled if one fasts on this Amavasya.[6]

Every month, the Amāvāsyā day is considered auspicious for the worship of forefathers and poojas are made. Religious people are not supposed to travel or work, and instead concentrate on the rites of Amavasyas, typically at home in the afternoon. Even today, traditional workers like masons do not work on Amavasya in India. However, they will work on Saturdays and Sundays. Even High Court judges of 18th century India used to observe Amavasya as a day off. It was the British Rule that brought the Christian Sunday-off principle to Indian industry.

On Amavasyas, Shraadh is done to forefathers by Brahmins whose fathers have died. In modern times, a short 20-minute version of the ceremony is done—offering black sesame and water as oblation to departed souls. This oblation is offered to father, grandfather, great-grandfather, mother, grandmother, and great-grandmother. If one of these persons are still alive, their name is skipped and the corresponding earlier generation person is offered oblation. Then a final oblation is offered to those anonymous souls which died and have nobody in their lineage offering oblation. These oblations are believed to give birth to good children without mental or physical challenges.

The dark fortnight of Aswayuja (September–October) is known as the Pitru Paksha (Mahalaya), which is especially sacred for offering oblations to departed ancestors. The last day of this period, the dark moon day, called mahalaya Amavasya, is considered the most important day in the year for performing obsequies and rites. The manes return to their abode on the evening of Deepavali. Due to the grace of the Yama, it has been ordained that offerings made during this period benefit all the departed souls, whether they are connected to you or not.

In Tamil Nadu, lakhs of People will make special Tharpanam (Oblation) in Rameshwaram & other Holy Theerthas on Thai Amavasai, Aadi Amavasai, Mahalaya Amavasai. Thai Amavasai comes in the month of Jan-Feb and is the 1st Amavasai after Uttranayana Punya Kaalam (Northern Journey of Sun). Aadi Amavasai comes in the month of Jul-Aug and is the 1st Amavasai after Dakshinayanam Punya Kaalam (Southern Journey of Sun). Pitru Paksh Mahalaya Amavasai comes during Navratri [7]

The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean.

Variance tells you the degree of spread in your data set. The more spread the data, the larger the variance is in relation to the mean.

The standard deviation is derived from variance and tells you, on average, how far each value lies from the mean. It’s the square root of variance.

Both measures reflect variability in a distribution, but their units differ:

Since the units of variance are much larger than those of a typical value of a data set, it’s harder to interpret the variance number intuitively. That’s why standard deviation is often preferred as a main measure of variability.

However, the variance is more informative about variability than the standard deviation, and it’s used in making statistical inferences.

Different formulas are used for calculating variance depending on whether you have data from a whole population or a sample.

When you have collected data from every member of the population that you’re interested in, you can get an exact value for population variance.

The population variance formula looks like this:

When you collect data from a sample, the sample variance is used to make estimates or inferences about the population variance.

The sample variance formula looks like this:

With samples, we use n – 1 in the formula because using n would give us a biased estimate that consistently underestimates variability. The sample variance would tend to be lower than the real variance of the population.

Reducing the sample n to n – 1 makes the variance artificially large, giving you an unbiased estimate of variability: it is better to overestimate rather than underestimate variability in samples.

It’s important to note that doing the same thing with the standard deviation formulas doesn’t lead to completely unbiased estimates. Since a square root isn’t a linear operation, like addition or subtraction, the unbiasedness of the sample variance formula doesn’t carry over the sample standard deviation formula.

You can calculate the variance by hand or with the help of our variance calculator below.

The variance is usually calculated automatically by whichever software you use for your statistical analysis. But you can also calculate it by hand to better understand how the formula works.

There are five main steps for finding the variance by hand. We’ll use a small data set of 6 scores to walk through the steps.

To find the mean, add up all the scores, then divide them by the number of scores.

Subtract the mean from each score to get the deviations from the mean.

Since x̅ = 50, take away 50 from each score.

Multiply each deviation from the mean by itself. This will result in positive numbers.

Add up all of the squared deviations. This is called the sum of squares.

Divide the sum of the squares by n – 1 (for a sample) or N (for a population).

Since we’re working with a sample, we’ll use  n – 1, where n = 6.

Variance matters for two main reasons:

Variance is important to consider before performing parametric tests. These tests require equal or similar variances, also called homogeneity of variance or homoscedasticity, when comparing different samples.

Uneven variances between samples result in biased and skewed test results. If you have uneven variances across samples, non-parametric tests are more appropriate.

Statistical tests like variance tests or the analysis of variance (ANOVA) use sample variance to assess group differences. They use the variances of the samples to assess whether the populations they come from differ from each other.

The main idea behind an ANOVA is to compare the variances between groups and variances within groups to see whether the results are best explained by the group differences or by individual differences.

If there’s higher between-group variance relative to within-group variance, then the groups are likely to be different as a result of your treatment. If not, then the results may come from individual differences of sample members instead.

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