Question

question 1 (1 point)
the numbers of points scored in each basketball game are 49, 36, 61, 64, 39, 41, 43, and 39.
find
a. minimum:
b. q1:
c. median:
d. q3:
e. maximum
f. in what percent of the games were at least 55 points scored?
g. are the data more spread out below the first quartile or above the third quartile? explain
h. find and interpret the interquartile range of the data.

Explanation:

Step1: Sort the data

$36,39,39,41,43,49,61,64$

Step2: Find minimum

The minimum is $36$.

Step3: Find Q1

Position of Q1: $\frac{n + 1}{4}=\frac{8+1}{4}=2.25$. So, $Q1 = 39$.

Step4: Find median

Position of median: $\frac{n+1}{2}=\frac{8 + 1}{2}=4.5$. Median $=\frac{41 + 43}{2}=42$.

Step5: Find Q3

Position of Q3: $\frac{3(n + 1)}{4}=\frac{3\times(8 + 1)}{4}=6.75$. So, $Q3=61$.

Step6: Find maximum

The maximum is $64$.

Step7: Percent of games with at least 55 points

2 out of 8 games had at least 55 points. $\frac{2}{8}\times100\% = 25\%$.

Step8: Spread analysis

Range below Q1: $39 - 36=3$. Range above Q3: $64 - 61 = 3$. Spread is the same.

Step9: Inter - quartile range

$IQR=Q3 - Q1=61 - 39 = 22$. It shows the spread of middle 50% of data.

Answer:

a. 36
b. 39
c. 42
d. 61
e. 64
f. 25%
g. Spread is the same.
h. 22; shows spread of middle 50% of data.