Final answer:
To compare the variability in the mean number of pages read by students in fourth grade and seventh grade, we can use the mean absolute deviation. The mean absolute deviation for fourth graders is 19.2, while the mean absolute deviation for seventh graders is 10. Therefore, the variability in the mean number of pages read by seventh graders is less than the variability in the mean number of pages read by fourth graders.
Step-by-step explanation:
To compare the variability in the mean number of pages read by fourth graders and seventh graders, we can use the mean absolute deviation. Mean absolute deviation is a measure of how spread out the data is around the mean. To calculate the mean absolute deviation, we first find the mean of the data set. Then, for each data point, we find the absolute difference between the data point and the mean, and calculate the mean of these absolute differences. Let's calculate the mean absolute deviation for both fourth graders and seventh graders:
Fourth Grade:
- Calculate the mean: (87 + 95 + 76 + 148 + 104) / 5 = 102
- Find the absolute difference between each data point and the mean: (|87 - 102| + |95 - 102| + |76 - 102| + |148 - 102| + |104 - 102|) / 5 = (15 + 7 + 26 + 46 + 2) / 5 = 96 / 5 = 19.2
- The mean absolute deviation for fourth graders is 19.2.
Seventh Grade:
- Calculate the mean: (183 + 187 + 204 + 215 + 196) / 5 = 197
- Find the absolute difference between each data point and the mean: (|183 - 197| + |187 - 197| + |204 - 197| + |215 - 197| + |196 - 197|) / 5 = (14 + 10 + 7 + 18 + 1) / 5 = 50 / 5 = 10
- The mean absolute deviation for seventh graders is 10.
Based on the mean absolute deviation, we can see that the variability in the mean number of pages read by seventh graders (10) is less than the variability in the mean number of pages read by fourth graders (19.2).