Question

i can summarize data sets. 4. mrs. wilson has her son benji chart the number of minutes he reads each day during the month of june. use the graph below to answer the questions. june minutes read a. how many more days did benji read 30 - 39 minutes than 0 - 9 minutes? b. the sum of which two intervals is equal to the number of days that benji read 20 - 29 minutes? c. which interval is likely to have the median number minutes read? why? d. which two intervals account for approximately 60% of benji’s reading? number of days 15 10 5 0 0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 number of minutes

Explanation:

Step1: Determine number of days in each interval

From the bar - graph:
Number of days in 0 - 9 minutes interval: 2
Number of days in 30 - 39 minutes interval: 11

Step2: Calculate the difference

To find how many more days Benji read 30 - 39 minutes than 0 - 9 minutes, we subtract the number of days in 0 - 9 minutes from the number of days in 30 - 39 minutes.
$11−2 = 9$

Step3: Analyze sums for part b

Number of days in 0 - 9 minutes interval: 2
Number of days in 10 - 19 minutes interval: 4
Number of days in 20 - 29 minutes interval: 7
Number of days in 30 - 39 minutes interval: 11
Number of days in 40 - 49 minutes interval: 3
$2 + 5=7$, so the sum of 0 - 9 and 10 - 19 intervals is equal to the number of days Benji read 20 - 29 minutes.

Step4: Find median for part c

The total number of days in June is $2 + 4+7 + 11+3=27$ days. The median is the 14th - ranked value when the data is ordered.
The first interval (0 - 9) has 2 days, the first two intervals (0 - 9 and 10 - 19) have $2 + 4 = 6$ days, the first three intervals (0 - 9, 10 - 19 and 20 - 29) have $2+4 + 7=13$ days, and the first four intervals (0 - 9, 10 - 19, 20 - 29 and 30 - 39) have $2+4 + 7+11 = 24$ days. So the median is in the 30 - 39 minutes interval.

Step5: Calculate percentage for part d

The total number of days is 27.
60% of 27 is $0.6\times27 = 16.2$
The 20 - 29 minutes interval has 7 days and the 30 - 39 minutes interval has 11 days, and $7 + 11=18$ which is approximately 60% of 27.

Answer:

a. 9
b. 0 - 9 and 10 - 19
c. 30 - 39 minutes, because when ordering the data, the 14th - ranked value (median of 27 data points) lies in this interval.
d. 20 - 29 and 30 - 39