| If the mean of the numbers 27 + x, 31 + x, 89 + x, 107 + x, 156 + x is 82, then the find the mean of 130 + x, 126 + x, 68 + x, 50 + x, 1 + x.
Sol: Given that, the mean of the numbers
27 + x, 31 + x, 89 + x, 107 + x, 156 + x is 82
⇒ 410 + 5x = 410
⇒ 5x = 0 ⇒ x = 0
∴ The required mean is
Recall that data is information in the form of numerical figures. To analyse data or compare one set of data with another, there is a need for single representative value of data. We have discussed earlier three such simple measures, namely – mean, median and mode. Geometric mean and harmonic mean are two other measures of central tendency. These give a rough picture of where the data points are centred. But in some cases, the variation in a set of data cannot be satisfactorily described by a single representative value or measure. A combination of measures is required to analyse data and draw meaningful conclusions.
Let us take up a practical example in a game of cricket, which may interest most of you. Assume that the scores of Virendra Sehwag (Mr Dashing) and Rahul Dravid (Mr Dependable) in ten innings are as under:
Now, how do you compare the performance of these two batsmen ?
The (arithmetic) mean or more simply the average is given by .
So the mean of Sehwag =
The mean of Dravid =
Coincidentally the means of both the players are same !