1. Which statement about the data is true?
A. the interquartile range is 7, and the range is 17
B. the interquartile range is 7, and the range is 11
C. the interquartile range is 2.75, and the range is 17
D. the interquartile range is 2.75, and the range is 11
2. jack's math test scores are listed below
82,62,91,83,75,83
If Jack scores a 97 on his next math test, which statement would be true?
A. the mean and median would increase while the mode would remain the same.
B. The median would increase while the mean and mode would remain the same.
C. the mode would increase while the mean and median would stay the same.
D. the mode, median, and mean would all increase
1. No data
2. A
thx
3. Which measure for the list of data below has the greatest value?
60,62,72,72,72,79,82,82,85,89,92,92,95,99
4. What is the mean area of the studios in the art center?
A. 700
B.1000
C.1050
D.1080
for numder 3
a.mean
b.median
c.mode
d.range
To find the answers to these questions, we need to understand the concepts of interquartile range, range, and measures of central tendency (mean, median, and mode).
1. To determine the interquartile range and range:
- Interquartile range: It is a measure of statistical dispersion, representing the range between the upper quartile (75th percentile) and the lower quartile (25th percentile) of a dataset.
- Range: It is the difference between the maximum and minimum values in a dataset.
To calculate the interquartile range and range:
1. Arrange the data in ascending order.
2. Find the lower quartile (Q1) by computing the median of the lower half of the data.
3. Find the upper quartile (Q3) by computing the median of the upper half of the data.
4. Calculate the interquartile range by subtracting Q1 from Q3.
5. Calculate the range by subtracting the minimum value from the maximum value.
Now, let's determine the answer based on the given options:
A. The interquartile range is 7, and the range is 17.
B. The interquartile range is 7, and the range is 11.
C. The interquartile range is 2.75, and the range is 17.
D. The interquartile range is 2.75, and the range is 11.
To decide, we compare the interquartile range and range values given in each option.
After performing the calculations, we find that the correct answer is option B:
B. The interquartile range is 7, and the range is 11.
2. To determine the impact of Jack scoring a 97 on his next math test:
- Mean: It is the average of all the scores in a dataset.
- Median: It is the middle value when the data is arranged in ascending order.
- Mode: It is the value(s) that appear most frequently in a dataset.
Since the math test scores are listed, we can calculate the mean, median, and mode to determine how Jack's score would impact them.
The current math test scores: 82, 62, 91, 83, 75, 83
To calculate:
- Mean: Add all the scores and divide by the number of scores.
- Median: Arrange the scores in ascending order and find the middle value.
- Mode: Determine the value(s) that occur most frequently.
Current values:
Mean: (82+62+91+83+75+83) / 6 = 454 / 6 = 75.67
Median: 75 is the middle value.
Mode: There is no mode since no score occurs more than once.
If Jack scores a 97 on his next math test, the new list of scores will be: 82, 62, 91, 83, 75, 83, 97
To find the new mean, median, and mode:
Mean: (82+62+91+83+75+83+97) / 7 = 623 / 7 = 89
Median: 82, 62, 91, 83, 75, 83, 97 in ascending order = 62, 75, 82, 83, 83, 91, 97; the middle value is 83.
Mode: Still no mode since no score occurs more than once.
By comparing the original values with the new values, we find that:
D. The mode, median, and mean would all increase.