Let's determine the missing value in the Grouped Frequency Distribution Table (GFDT) step-by-step.
1. Identify the total number of students [tex]\( n \)[/tex]:
From the cumulative frequency table, we see that the cumulative frequency "less than 200" represents the total number of students who took the test. This value, [tex]\( n \)[/tex], is 100.
2. Understand the cumulative frequencies:
- "Less than 150": 19
- "Less than 160": 34
- "Less than 170": 44
- "Less than 180": 55
- "Less than 190": 70
3. Infer the cumulative frequency to find the missing frequency:
The cumulative frequency "less than 180" is 55. This means that 55 students scored less than 180. The cumulative frequency "less than 170" is 44, which means that 44 students scored less than 170.
4. Calculate the frequency for the interval 170-179:
To find the frequency for the range 170-179, subtract the cumulative frequency "less than 170" from the cumulative frequency "less than 180":
[tex]\[
\text{Frequency for 170-179} = \text{Cumulative frequency for less than 180} - \text{Cumulative frequency for less than 170}
\][/tex]
[tex]\[
\text{Frequency for 170-179} = 55 - 44 = 11
\][/tex]
So, the missing value in the GFDT for the score range 170-179 is [tex]\( \boxed{11} \)[/tex].
