Question

below are iq scores from 30 randomly selected adults. { 60, 63, 78, 81, 83, 84, 85, 91, 92, 93, 94, 97, 98, 98, 98, 99, 101, 102, 103, 107, 109, 109, 110, 112, 113, 114, 114, 121, 121, 125 }. first, give the mean of the data set. 103 next, give the median of the data set.

Explanation:

Step1: Calculate sum of data

Sum all the IQ - scores: $60 + 63+78 + 81+83+84+85+91+92+93+94+97+98+98+98+99+101+102+103+107+109+109+110+112+113+114+114+121+121+125=2970$

Step2: Calculate the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 30$ and $\sum_{i=1}^{n}x_{i}=2970$. So, $\bar{x}=\frac{2970}{30}=99$

Step3: Find the median

Since $n = 30$ (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. First, the data is already in ascending order. $\frac{n}{2}=15$ and $\frac{n}{2}+1 = 16$. The 15th value is 98 and the 16th value is 99. The median $M=\frac{98 + 99}{2}=98.5$

Answer:

Mean: 99
Median: 98.5