Question

The data shown represent the number of runs made each year during Bill Mazeroski’s career. Check for normality.

30 59 69 50 58 71 55 43 3

66 52 56 62 36 13 29 17 31

Answer 1

Answer:

The given data is not normal.

Step-by-step explanation:

We are given the following data:

30, 59, 69, 50, 58, 71, 55, 43, 3,  66, 52, 56, 62, 36, 13, 29, 17, 31

Condition for normality:

Mean = Mode = Median

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{800}{18} = 44.44$

Mode is the most frequent observation of the data.

Since all the value appeared once, there is no mode.

$Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}$

Sorted data: 3, 13, 17, 29, 30, 31, 36, 43, 50, 52, 55, 56, 58, 59, 62, 66, 69, 71

Median =

$=\dfrac{9^{th}+10^{th}}{2} = \dfrac{50+52}{2}=51$

Since the mean, mode and median of data are not equal, the data is not normal.