The table shows the wages in US dollars earned by technical developers in an ICT firm. Given that the mean…

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The table shows the wages in US dollars earned by technical developers in an ICT firm. Given that the mean wage is 27 rac1116 USD, find the value of a.

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here's the solution for question 17. Question 17: The table below shows the wages in US dollars earned by technical developers in an ICT firm. Amount (USD) — 10 − 14 — 15 − 24 — 25 − 29 — 30 − 44 — 45 − 64Number of workers — 6 — 16 — a — 10 — 5 (a) Given that the mean wage is 27 11/16 USD, find the value of a. Step 1: Calculate the midpoint (x) for each class. For grouped data, the mean is given by the formula: Mean = (∑ (f × x))/(∑ f). Class (Amount USD) — Frequency (f) — Midpoint (x) — f × x10 - 14 — 6 — (10+14)/(2) = 12 — 6 × 12 = 72; 15 − 24 — 16 — (15+24)/(2) = 19.5 — 16 × 19.5 = 312; 25 − 29 — a — (25+29)/(2) = 27 — a × 27 = 27a; 30 − 44 — 10 — (30+44)/(2) = 37 — 10 × 37 = 370; 45 − 64 — 5 — (45+64)/(2) = 54.5 — 5 × 54.5 = 272.5 Step 2: Calculate the sum of frequencies (∑ f) and the sum of (f × x) (∑ (f × x)). ∑ f = 6 + 16 + a + 10 + 5 = 37 + a; ∑ (f × x) = 72 + 312 + 27a + 370 + 272.5 = 1026.5 + 27a Step 3: Set up the equation for the mean. The given mean wage is 27 11/16 USD. 27 11/16 = (27 × 16 + 11)/(16) = (432 + 11)/(16) = 443/16 Using the mean formula: (1026.5 + 27a)/(37 + a) = 443/16 Step 4: Solve for a. Cross-multiply: 16(1026.5 + 27a) = 443(37 + a); 16424 + 432a = 16391 + 443a Subtract 432a from both sides: 16424 = 16391 + 443a − 432a; 16424 = 16391 + 11a Subtract 16391 from both sides: 16424 − 16391 = 11a; 33 = 11a; a = 33/11; a = 3 The value of a is 3. (b) Find the median class and its frequency. Step 1: Use the value of a=3 to list the frequencies and calculate the total number of workers. Frequencies: 6, 16, 3, 10, 5. Total number of workers (∑ f) = 6 + 16 + 3 + 10 + 5 = 40. Step 2: Determine the position of the median. The median position is (∑ f)/(2) = 40/2 = 20^(th) value. Step 3: Calculate the cumulative frequencies to find the median class. Class (Amount USD) — Frequency (f) — Cumulative Frequency (cf)10 - 14 — 6 — 6 15 − 24 — 16 — 6 + 16 = 22; 25 − 29 — 3 — 22 + 3 = 25; 30 − 44 — 10 — 25 + 10 = 35; 45 − 64 — 5 — 35 + 5 = 40 The 20^(th) value falls into the class where the cumulative frequency first exceeds or equals 20. This is the class 15 − 24, which has a cumulative frequency of 22. The median class is 15 − 24. The frequency of the median class is 16. (c) On the grid provided, draw a histogram to represent the information. To draw a histogram for this data, you would follow these steps: 1. Determine Class Boundaries: Adjust the class intervals to be continuous. For example, 10-14 becomes 9.5-14.5, 15-24 becomes 14.5-24.5, and so on. 2. Calculate Class Widths: The width of each class interval (e.g., 14.5 − 9.5 = 5). 3. Calculate Frequency Densities: Since the class widths are not uniform, you need to calculate frequency density for each class using the formula: Frequency Density = FrequencyClass Width. 10-14: 6/5 = 1.2; 15-24: 16/10 = 1.6; 25-29: 3/5 = 0.6 30-44: 10/15 ≈ 0.67 45-64: 5/20 = 0.25 4. Draw Axes: The x-axis represents the Amount (USD) using the class boundaries. The y-axis represents the Frequency Density. 5. Draw Bars: For each class, draw a rectangular bar with a width corresponding to its class width and a height corresponding to its frequency density. The bars should touch each other.

Class (Amount USD)	Frequency ( $f$ )	Midpoint ( $x$ )	$f \times x$
10 - 14	6	$\frac{10+14}{2} = 12$	$6 \times 12 = 72$
15 - 24	16	$\frac{15+24}{2} = 19.5$	$16 \times 19.5 = 312$
25 - 29	a	$\frac{25+29}{2} = 27$	$a \times 27 = 27a$
30 - 44	10	$\frac{30+44}{2} = 37$	$10 \times 37 = 370$
45 - 64	5	$\frac{45+64}{2} = 54.5$	$5 \times 54.5 = 272.5$

Class (Amount USD)	Frequency ( $f$ )	Cumulative Frequency (cf)
10 - 14	6	6
15 - 24	16	$6 + 16 = 22$
25 - 29	3	$22 + 3 = 25$
30 - 44	10	$25 + 10 = 35$
45 - 64	5	$35 + 5 = 40$

The table shows the wages in US dollars earned by technical developers in an ICT firm. Given that the mean wage is 27 rac1116 USD, find the value of a.

Answers

Step-by-step solution

Part 17

Part a· 4 steps3

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

Calculate the sum of frequencies ( $\sum f$ ) and the sum of ( $f \times x$ ) ( $\sum (f \times x)$ ).

Set up the equation for the mean.

Solve for $a$ .

Part b· 3 steps15 - 24

Use the value of $a=3$ to list the frequencies and calculate the total number of workers.

Determine the position of the median.

Calculate the cumulative frequencies to find the median class.

Part c

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More Mathematics Questions

The table shows the wages in US dollars earned by technical developers in an ICT firm. Given that the mean wage is 27 rac1116 USD, find the value of a.

Answers

Step-by-step solution

Part 17

Part a· 4 steps3

Calculate the midpoint (xxx) for each class.

Calculate the sum of frequencies (∑f\sum f∑f) and the sum of (f×xf \times xf×x) (∑(f×x)\sum (f \times x)∑(f×x)).

Set up the equation for the mean.

Solve for aaa.

Part b· 3 steps15 - 24

Use the value of a=3a=3a=3 to list the frequencies and calculate the total number of workers.

Determine the position of the median.

Calculate the cumulative frequencies to find the median class.

Part c

Try one yourself

Still stuck on this one?

More Mathematics Questions

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

Calculate the sum of frequencies ( $\sum f$ ) and the sum of ( $f \times x$ ) ( $\sum (f \times x)$ ).

Solve for $a$ .

Use the value of $a=3$ to list the frequencies and calculate the total number of workers.