The table shows the number of calls received by a call centre in a day. Calculate the mean number of calls…

Question

The table shows the number of calls received by a call centre in a day. Calculate the mean number of calls per day.

ScanSolve AI Tutor · Accepted Answer

I've interpreted the table and questions from your image. Here is the data from the table: Number of calls per day (Class Interval) — Frequency (f) — Midpoint (x) — fx1-10 — 4 — 5.5 — 22.0 11-20 — 8 — 15.5 — 124.0 21-30 — 12 — 25.5 — 306.0 31-40 — 15 — 35.5 — 532.5 41-50 — 10 — 45.5 — 455.0 51-60 — 7 — 55.5 — 388.5 61-70 — 5 — 65.5 — 327.5 71-80 — 3 — 75.5 — 226.5 81-90 — 2 — 85.5 — 171.0 91-100 — 1 — 95.5 — 95.5 Total — ∑ f = 67 — ∑ fx = 2648.5 a) From the table above: i) State the modal class. Step 1: Identify the highest frequency in the table. The highest frequency is 15. Step 2: Identify the class interval corresponding to the highest frequency. The class interval corresponding to a frequency of 15 is 31-40. The modal class is 31-40. ii) State the modal frequency. Step 1: Identify the highest frequency in the table. The highest frequency is 15. The modal frequency is 15. b) Use the table above to calculate the mean of the number of calls per day. Step 1: Calculate the midpoint (x) for each class interval. The midpoint is calculated as (lower limit + upper limit) / 2. These are shown in the table above. Step 2: Calculate the product of frequency and midpoint (fx) for each class interval. These values are shown in the table above. Step 3: Calculate the sum of all frequencies (∑ f). ∑ f = 4 + 8 + 12 + 15 + 10 + 7 + 5 + 3 + 2 + 1 = 67 Step 4: Calculate the sum of all fx values (∑ fx). ∑ fx = 22.0 + 124.0 + 306.0 + 532.5 + 455.0 + 388.5 + 327.5 + 226.5 + 171.0 + 95.5 = 2648.5 Step 5: Use the formula for the mean of grouped data. The mean (x) is given by: x = (∑ fx)/(∑ f); x = 2648.5/67 x ≈ 39.52985 Step 6: Round the mean to an appropriate number of decimal places (e.g., two decimal places). x ≈ 39.53 The mean of the number of calls per day is 39.53.

The table shows the number of calls received by a call centre in a day. Calculate the mean number of calls per day.

Answers

Step-by-step solution

Part a(i)· 2 steps

Identify the highest frequency in the table.

Identify the class interval corresponding to the highest frequency.

Part a(ii)· 1 step
$\text{15}$

Identify the highest frequency in the table.

Part b· 6 steps
$\text{39.53}$

Calculate the midpoint ( $x$ ) for each class interval.

Calculate the product of frequency and midpoint ( $fx$ ) for each class interval.

Calculate the sum of all frequencies ( $\sum f$ ).

Calculate the sum of all $fx$ values ( $\sum fx$ ).

Use the formula for the mean of grouped data.

Round the mean to an appropriate number of decimal places (e.g., two decimal places).

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The table shows the number of calls received by a call centre in a day. Calculate the mean number of calls per day.

Answers

Step-by-step solution

Part a(i)· 2 steps

Identify the highest frequency in the table.

Identify the class interval corresponding to the highest frequency.

Part a(ii)· 1 step15\text{15}15

Identify the highest frequency in the table.

Part b· 6 steps39.53\text{39.53}39.53

Calculate the midpoint (xxx) for each class interval.

Calculate the product of frequency and midpoint (fxfxfx) for each class interval.

Calculate the sum of all frequencies (∑f\sum f∑f).

Calculate the sum of all fxfxfx values (∑fx\sum fx∑fx).

Use the formula for the mean of grouped data.

Round the mean to an appropriate number of decimal places (e.g., two decimal places).

Try one yourself

Still stuck on this one?

More Mathematics Questions

Part a(ii)· 1 step
$\text{15}$

Part b· 6 steps
$\text{39.53}$

Calculate the midpoint ( $x$ ) for each class interval.

Calculate the product of frequency and midpoint ( $fx$ ) for each class interval.

Calculate the sum of all frequencies ( $\sum f$ ).

Calculate the sum of all $fx$ values ( $\sum fx$ ).