Question

A psychologist is interested in the social interactions of preschool children. She measures the number of verbal interactions that each child at a preschool engages in during a day. The frequency distribution of the data is listed in the table below.

Class Interval	Frequency
6 - 15	1
16 - 25	2
26 - 35	3
36 - 45	3
46 - 55	4
56 - 65	10
66 - 75	7
76 - 85	6
86 - 95	4
96 - 105	5

Q1. What is the percentile rank of a score of 60 (input the answer using 2 decimal places, do not use the % symbol)?

Q2. Using the 2k rule, what is the best number of intervals to use when having a set of 60 scores?

Q3. A set of data has the following characteristics:

- All the scores are whole numbers,

- The range is 90,

- It has been decided to use 10 intervals.

What is the interval or class width to be used?

Q4. A set of data has the following characteristics:

- Scores smallest place value are hundredths,

- The range is 72,

- It has been decided to use 7 intervals.

What is the interval or class width to be used?

Q5. A set of data has the following characteristics:

- All the scores are whole numbers,

- There are 120 scores,

- The range is 40,

- Intervals of width 10 are needed.

What is the number of intervals needed?

Q6. A set of data has the following characteristics:

- All scores are whole numbers,

- The lowest score is 20,

- The highest score is 50,

- It has been decided to use 5 intervals of width 7,

If ideal intervals are needed, the starting point or lower limit of the 1st interval should be (1)——— and the final point or higher limit of the last interval should be (2)———

Answer 1

Answer: A psychologist is interested in the social interactions of preschool children. She measures the number of verbal interactions that each child at a preschool engages in during a day. The frequency distribution of the data is listed in the table below.

Solution:

Q1. What is the percentile rank of a score of 60.

Class Interval	Frequency	Cumulative frequency
6 - 15	1	1
16 - 25	2	3
26 - 35	3	6
36 - 45	3	9
46 - 55	4	13
56 - 65	10	23
66 - 75	7	30
76 - 85	6	36
86 - 95	4	40
96 - 105	5	45

cumulative freq for the 60% percentile = 45 * 0.60 = 27

the value 27 is located in the class (66 - 75)

P60 = lower + Lp + previous cumulative frequency /frequency * Class width

P60 = 66 + (27 - 23)/7 * (75-66)

P60 = 71.1428

Therefore, the percentile rank of score of 60 is 71.14.

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