Estimated mean from a grouped table

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Walkthrough to print

  1. Work out the mean number of pets.

    Pets0123
    Frequency6842
    1.1

  2. Work out the mean number of tries.

    Tries1234
    Frequency7652
    2.1

  3. 25 people rate a film. 4 give it 1 star, 9 give it 2 stars and the rest give it 3 stars. Work out the mean number of stars.

    2.32

Ollie's walk to school takes between 10 and 20 minutes.

What one number would you give for how long it takes? Why?

15 minutes: halfway

Midpoint
The value halfway between the two ends of a class.

Find the midpoint

0 < t ≤ 10 5

Find the midpoint

20 < t ≤ 30 25

Find the midpoint

5 < t ≤ 10 7.5

  1. Find the midpoint of 40 < t ≤ 60.

    50

  2. Find the midpoint of 0 < m ≤ 5.

    2.5

  3. Find the midpoint of 15 < h ≤ 30.

    22.5

  4. A class starts at 30 and its midpoint is 35. Where does the class end?

    40

Estimated mean

  1. MidpointHalfway between the two ends of each class.
  2. Frequency × midpointMultiply each frequency by its midpoint.
  3. TotalsAdd up the frequency column and the f × x column.
  4. DivideDivide the total of f × x by the total frequency.
Mean ≈ total f × xtotal frequency
(lower + upper) ÷ 2
frequency × midpoint, on every row
not the midpoint column
an estimate: the exact values are not known
Walkthrough to print

Estimate the mean.

Time, t (min)FrequencyMidpointf × x
0 < t ≤ 103515
10 < t ≤ 2051575
20 < t ≤ 3022550
Total10140
Mean ≈140÷10
Estimated mean14 min

Estimate the mean.

Time, t (min)FrequencyMidpointf × x
0 < t ≤ 102510
10 < t ≤ 2061590
20 < t ≤ 3022550
Total10150
Mean ≈150÷10
Estimated mean15 min

Estimate the mean.

Time, t (min)FrequencyMidpointf × x
0 < t ≤ 103515
10 < t ≤ 2051575
20 < t ≤ 3022550
Total10140
Mean ≈140÷10
Estimated mean14 min

Estimate the mean.

Time, t (min)FrequencyMidpointf × x
0 < t ≤ 2011010
20 < t ≤ 40530150
40 < t ≤ 60450200
Total10360
Mean ≈360÷10
Estimated mean36 min

Estimate the mean.

Time, t (min)FrequencyMidpointf × x
0 < t ≤ 103515
10 < t ≤ 2051575
20 < t ≤ 3022550
Total10140
Mean ≈140÷10
Estimated mean14 min

Estimate the mean.

Width, w (cm)FrequencyMidpointf × x
0 < w ≤ 45210
4 < w ≤ 88648
8 < w ≤ 1231030
Total1688
Mean ≈88÷16
Estimated mean5.5 cm

Estimate the mean.

Time, t (min)FrequencyMidpointf × x
0 < t ≤ 103515
10 < t ≤ 2051575
20 < t ≤ 3022550
Total10140
Mean ≈140÷10
Estimated mean14 min

Estimate the mean.

Height, h (cm)FrequencyMidpointf × x
100 < h ≤ 1203110330
120 < h ≤ 1406130780
140 < h ≤ 160101501500
160 < h ≤ 18061701020
Total253630
Mean ≈3630÷25
Estimated mean145.2 cm

Estimate the mean.

Time, t (min)FrequencyMidpointf × x
0 < t ≤ 103515
10 < t ≤ 2051575
20 < t ≤ 3022550
Total10140
Mean ≈140÷10
Estimated mean14 min

Estimate the mean.

Mass, m (g)FrequencyMidpointf × x
0 < m ≤ 562.515
5 < m ≤ 151010100
15 < m ≤ 30422.590
Total20205
Mean ≈205÷20
Estimated mean10.25 g

  1. The frequencies are 4 and 6. The midpoints are 5 and 15. Find the total of frequency × midpoint.

    110

  2. The total of frequency × midpoint is 380. The total frequency is 20. Estimate the mean.

    19

  3. The total of frequency × midpoint is 510. The total frequency is 20. Estimate the mean.

    25.5

  4. What do we call the class with the highest frequency?

    The modal class

Estimated mean from a grouped table worksheet, page 1

Answer sheet

  1. The estimated mean of 20 values is 16. What is the total of frequency × midpoint?

    320

  2. Sam divides the total of frequency × midpoint by the number of classes. What should he divide by?

    The total frequency

  1. Find the midpoint of 20 < m ≤ 35.

    27.5

  2. The table shows the times some people took. Estimate the mean time.

    17.5 min
    Time (t min)Frequency0 < t ≤ 10410 < t ≤ 20920 < t ≤ 30530 < t ≤ 402

  3. Tom works out the total of frequency × midpoint for a table with 5 classes. He divides it by 5. Explain his mistake.

    Divide by the total frequency
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