Question

an intelligence test was recently administered to a group of 10 people. their respective completion times (in minutes) were as follows. 32, 42, 40, 38, 31, 36, 37, 27, 34, 26 (a) what is the mean of this data set? if your answer is not an integer, round your answer to one decimal place. (b) what is the median of this data set? if your answer is not an integer, round your answer to one decimal place. (c) how many modes does the data set have, and what are their values? indicate the number of modes by clicking in the appropriate circle, and then indicate the value(s) of the mode(s), if applicable.

Explanation:

Step1: Calculate the sum of data

$32 + 42+40 + 38+31+36+37+27+34+26=343$

Step2: Calculate the mean

The number of data points $n = 10$. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}=\frac{343}{10}=34.3$

Step3: Arrange data in ascending order

$26,27,31,32,34,36,37,38,40,42$

Step4: Calculate the median

Since $n = 10$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. $\frac{n}{2}=5$, $\frac{n}{2}+1 = 6$. The median $M=\frac{34 + 36}{2}=35$

Step5: Determine the mode

Each value in the data - set $26,27,31,32,34,36,37,38,40,42$ appears only once. So, there are zero modes.

Answer:

(a) $34.3$
(b) $35$
(c) zero modes