Question

5.16a,b,c,d tei paper - pencil practice

1. the number of cartons of apples sold at a store each day for eight days is shown.

30, 40, 51, 30, 34, 20, 30, 45
determine the value for each statistical measure.
mean
median
mode
range
30 31 35 32

1. the number of fifth - graders buying lunch each day for nine days is shown.

90, 72, 48, 84, 77, 72, 50, 83
determine the value for each statistical measure.

Explanation:

Step1: Calculate the mean for the first - set of data

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 8$, and $\sum_{i=1}^{8}x_{i}=30 + 40+51 + 30+34+20+30+45=280$. So, $\bar{x}=\frac{280}{8}=35$.

Step2: Calculate the median for the first - set of data

First, order the data: $20,30,30,30,34,40,45,51$. Since $n = 8$ (even), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th values. The $\frac{8}{2}=4$th value is $30$ and the $(\frac{8}{2}+1)=5$th value is $34$. So, the median is $\frac{30 + 34}{2}=32$.

Step3: Calculate the mode for the first - set of data

The mode is the number that appears most frequently. In the data set $30,40,51,30,34,20,30,45$, the number $30$ appears $3$ times, more frequently than any other number, so the mode is $30$.

Step4: Calculate the range for the first - set of data

The range is the difference between the maximum and minimum values. The maximum value is $51$ and the minimum value is $20$. So, the range is $51-20 = 31$.

Answer:

Mean: $35$
Median: $32$
Mode: $30$
Range: $31$