Name ___________________________ 7-6 NotesIB Math SL

Lesson 7-6 Cumulative Frequency Graphs/Review

Learning Goal: How do we interpret cumulative frequency graphs? What have we learned about statistics thus far?

Quick Facts and Definitions CUMULATIVE FREQUENCY – a running total of the given data

PERCENTILE – is the score below which a certain percentage of data liesFor example:

- If you are in the 90th percentile for your height that means that …

- If you are in the 50th percentile for SAT scores that means that …

Lower Quartile (Q1)- is the 25th percentile

Median (Q2) – is the 50th percentile

Upper Quartile (Q3) – is the 75th percentile

Let’s try a couple more together!

1. The accompanying table shows the weights, in pounds, for the students in an IB Math Studies SL class.

Interval Frequency

90≤w<100 6

100≤w<110 3

110≤w<120 0

120≤w<130 3

130≤w<140 0

140≤w<150 2

150≤w<160 2

a) Construct a cumulative frequency table by adding a column to the given table.

b) How many students weigh less than 150 pounds?

c) How many students weigh more than 130 pounds?

d) What is the average weight?

2. There are 120 teachers in a school. Their ages are represented by the cumulative frequency graph below.

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5A g e

1 3 0

1 2 0

11 0

1 0 0

9 0

8 0

7 0

6 0

5 0

4 0

3 0

2 0

1 0

0

Cum

ulat

ive

freq

uenc

y

a) Determine the median (50th percentile).

b) What is the 40th percentile?

c) What is the 95th percentile?

d) What is the 70th percentile?

3.

Steps to find a percentile

1. Take the percentile you wish to find and multiply that by your sample size.

2. Go to this value on the Cumulative Frequency Axis

3. Go straight ACROSS to the Cumulative Frequency Curve, when you hit it go straight DOWN.

4. Read the value on the x-axis, this is the percentile!

Group Work/ Quiz Review (will be collected tomorrow before quiz!)

1. Three positive integers a, b, and c, where a < b < c, are such that their median is 11, their mean is 9 and their range is 10. Find the value of a.

2. The table shows the scores of competitors in a competition.

Score 10 20 30 40 50

Number of competitors with this score 1 2 5 k 3

The mean score is 34. Find the value of k.

3. The following table shows the mathematics marks scored by students.

Mark 1 2 3 4 5 6 7

Frequency 0 4 6 k 8 6 6

The mean mark is 4.6.

(a) Find the value of k.

(b) Write down the mode.

4.

5. At a conference of 100 mathematicians there are 72 men and 28 women. The men have a mean height of 1.79 m and the women have a mean height of 1.62 m. Find the mean height of the 100 mathematicians.

6.

c) There are 60 data values in the set. Estimate the number of values that are less than 10.

7.

8.

9.

10. From January to September, the mean number of car accidents per month was 630. From October to December, the mean was 810 accidents per month.

What was the mean number of car accidents per month for the whole year?

11.

12.