Question

hint 1 hint 2 hint 3 hint 4 hint 5
below are iq scores from 30 randomly selected adults.
{ 78, 82, 88, 88, 89, 93, 97, 98, 98, 98, 100, 101, 101, 102, 103, 104, 106, 106, 107, 109, 110, 115, 116, 118, 118, 119, 119, 122, 128, 130 }.
first, give the mean of the data set.
104
×
part 2 of 6
next, give the median of the data set.

Explanation:

Step1: Calculate sum of data

Sum all the 30 IQ - scores: $78 + 82+88 + 88+89+93+97+98+98+98+100+101+101+102+103+104+106+106+107+109+110+115+116+118+118+119+119+122+128+130=3120$

Step2: Calculate the mean

The mean $\bar{x}=\frac{\text{Sum of data}}{\text{Number of data points}}$. Here, the number of data points $n = 30$. So, $\bar{x}=\frac{3120}{30}=104$

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. $\frac{n}{2}=\frac{30}{2}=15$ and $\frac{n}{2}+1 = 16$. The 15th value is 103 and the 16th value is 104. The median $M=\frac{103 + 104}{2}=103.5$

Answer:

103.5