The estimated mean score of the 50 grade 7 students in the first quarter examination is 42.54.
The frequency distribution table shows the distribution of scores of 50 grade 7 students in the first quarter examination. The table shows the number of students who scored within each class interval. The class intervals are grouped into equal ranges of 5 points, starting from 16-22 and ending with 44-50.
The frequency distribution table can be used to calculate the estimated mean of the scores. The estimated mean is calculated by taking the average of the midpoints of each class interval, weighted by the frequency of students in each class interval. The following formula is used to calculate the estimated mean:
Estimated mean = (sum of frequencies * midpoints) / total number of students
To calculate the estimated mean, we first need to find the midpoint of each class interval. The midpoint is the average of the upper and lower limits of each class interval. For example, the midpoint of the class interval 16-22 is (16 + 22) / 2 = 19.
Next, we need to multiply the midpoint of each class interval by the frequency of students in that class interval. For example, the frequency of students in the class interval 16-22 is 4. Therefore, the product of the midpoint and frequency for this class interval is 4 * 19 = 76.
Finally, we need to add up the products of the midpoints and frequencies for all class intervals and divide by the total number of students. The following table shows the calculation of the estimated mean:
Class interval Midpoint Frequency Product of midpoint and frequency
44-50 47 6 282
37-43 40 27 1080
30-36 33 13 429
23-29 26 10 260
16-22 19 4 76
Total 50 2127
Estimated mean = 2127 / 50 = 42.54
Therefore, the estimated mean score of the 50 grade 7 students in the first quarter examination is 42.54.