## Purusottam Mishra is teaching live on Unacademy Plus

STATISTICS MEASURE OF CENTRAL TENDENNCY MEAN - MEDIAN - MODE

CENTRAL TENDENCY A measure of central tendency is a single value that describes the way in which a group of data cluster around a central value. There are three measures of central tendency: the mean, the median, and the mode. It may also be called a center or location of the distribution. Mean, median, and mode are three kinds of "averages".

Mean (Arithmetic The mean (or average) is the most popular and well known measure of central tendency. It can be used with both discrete and continuous data . The mean is equal to the sum of all the values in the data set divided by the number of values in the data cat Cn ifi^10, hav n ,al'iae in a data set and thev have ted (x1 +x2++xn) Cx

When not to use the mean? Staff 1 2 3 5 6 7 8 9 10 Salary 15k 18k 16k 14k 15k 15k 12k 17k 90k 95k .The mean has one main disadvantage: .it is particularly susceptible to the influence of outliers. Mean value might not be the best way to accurately reflect the salary of a worker, as most workers have salaries in the $12k to 18k range. The mean is being skewed by the two large However, as the data becomes skewed the mean loses its abilit to provide the best central location for the data because the ske data is dragging it away from the typical value. However, the median best retains this position and is not as str

The median is the middle score for a set of data that has been arranged in order of magnitude. The median is less affected by outliers and skewed data. To find the median: Arrange the data points from smallest to largest. If the number of data points is odd, the median is the middle data point in the list. lf the number of data points is even, the median is the average of the two middle data points in

It can, however, be explained like this: Median (odd set of numbers) - ((n+1)/2)th term Median (even set of numbers) - (2)hterm (3 1)hterm 2 Median 65 55 89 56 3514 56 55 87 45 92 We first need to rearrange that data into order of magnitude (smallest first): 14 35 45 55 55 56 56 65 87 89 92 Q. Finc

MODE The mode is the most commonly occurring data point in a dataset. The mode is the most frequent score in our data set. #Finding the mode The mode is useful when there are a lot of repeated values in a dataset. There can be no mode, one mode, or multiple modes in a dataset.

. The mode is very rarely used with continuous data because of multiple values and . It will not provide us with a very good measure of central tendency when the most common mark is far away from the rest of the data in the data set. RANGE Range, which is the difference between the largest and smallest value in the data set o it describes how well the central tendency

QUESTIONS: . Q.1. Find the mean, median, mode, and range for the following list of values: 13, 18, 13, 14, 13, 16, 14, 21, 13 Ans Mean_:-The mean is the usual average, so l'll add and then divide: . (13 + 1813 +14 13 16 +14 21 13)+ 9 = 15 Note The mean, in this case, isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your

Median . The median is the middle value, so first l'll have to rewrite the list in numerical order: . 13, 13, 13, 13, 14, 14, 16, 18, 21 There are nine numbers in the list, so the middle one will be the (9 + 1) + 2 10 - 2 5th number: . 13, 13, 13, 13, 14, 14, 16, 18, 21 So the median is 14.

Q. A studeht has dotteh the Tollowind grades oh his tests: 87, 95, 76, and 88. He wants an 85 or better overall. What is the minimum grade he must get on the last test in order to achieve that average?

Value Frequency 20 29 30 39 2 4 4 3 2 40 116 120 Mean of the distribution - 481 15 -32.1 (Answer rounded to the tenth).