Question

1. Consider the data presented below of a dataset of midterm exam scores from last year’s stats class. Do the following:
2. Group them into a frequency distribution employing a class width of i = 10.
3. Create a summary table showing:
   1. The class intervals
   2. The upper and lower real limits of each class interval
   3. The midpoints of each class interval
   4. The grouped frequency distribution of each class interval
   5. The cumulative frequency for each class interval
   6. The cumulative proportion of each class interval
   7. The cumulative percentage of each class interval
   8. Draw a frequency polygon and histogram representing the grouped frequency distribution
4. Based on the table you created, answer the following questions:
5. 1. How many scores fall below the score of 80? (1pt)
6. 2. What proportion of scores fall below the score of 80? (1pt)
7. 3. What proportion of students scored 60 through 69? (1pt)
8. 4. What proportion of students scored above 89? (1pt)
9. 5. How many students scored above 89? (1pt)

RAW DATA:

79 51 67 50 78 62 89 83 73 80 88 48 60 71 79 89 63 55 93 71 41 81 46 50 61 59 50 90 75 61 75 98 53 79 80 70 73 42 72 74 67 73 79 67 85 91 67 77 74 77

i = 10 (5pts)

Class Interval              LRL – URL                   Midpoint                       f              Cf           Cp        C%

40 – 49

Draw a Frequency Polygon Here (3pts):

2. For the following grouped frequency distribution of test scores, determine the cumulative frequency and answer the following questions:

1. In this example, i is equal to __________. (1pt)

2. What is the upper and lower real limits of the class interval with a frequency of 75? (1pt)

3. Provide an interpretation of the Cf for class interval of 43-47. (1pt)

4. How many participants/scores are there? Meaning, if this is a sample, n = ____. (1pt)

Class Interval                                   f                       Cf

73 – 77                                              21

68 – 72                                              35

63 – 67                                              57

58 – 62                                              75

53 – 57                                              89

48 – 52                                              80

43 – 47                                              71

38 – 42                                              43

33 – 37                                              22

28 – 32                                              11

Answer 1

Q-2.,

(a) i refers to class width

= 77-73+1 = 5

(b)

Upper True Limit: Add a 5 to the decimal place to the right of the last number appearing in the highest value specified by the number in the class interval.

Lower True Limit: Subtract a 5 to the decimal place to the right of the last number appearing in the lowest value specified by the number in the class interval.

Here class interval corresponding to f=75 is 58-62

So  upper real limits = 62.5

and lower real limits= 57.5

(c)

The whole frequency of all classes less than the upper class boundary of a specified class is called the cumulative frequency of that class.

for 43-47, cf=21+35+57+75+89+80+71=428

So there are 428 scores greater than 47.

(d)

n=cumulative frequency of interval 28-32

= sum of all the frequencies

= 504