calculate the number of years, months and days from 1st Jan 2015 to 23rd July 2023, with 365 days to a year…

Question

calculate the number of years, months and days from 1st Jan 2015 to 23rd July 2023, with 365 days to a year and 30 days to a month.

ScanSolve AI Tutor · Accepted Answer

Here is the solution for Question 2: The table shows the distribution of marks obtained by 40 students: Marks (x) — Number of students (f)1-5 — 2 6-10 — 4 11-15 — 10 16-20 — 12 21-25 — 8 26-30 — 4 a) Calculate the mean mark. Step 1: Determine the midpoint (x) for each class interval and calculate fx. Marks — f — Midpoint (x) — fx1-5 — 2 — (1+5)/(2) = 3 — 2 × 3 = 6; 6-10 — 4 — (6+10)/(2) = 8 — 4 × 8 = 32; 11-15 — 10 — (11+15)/(2) = 13 — 10 × 13 = 130; 16-20 — 12 — (16+20)/(2) = 18 — 12 × 18 = 216; 21-25 — 8 — (21+25)/(2) = 23 — 8 × 23 = 184; 26-30 — 4 — (26+30)/(2) = 28 — 4 × 28 = 112 Step 2: Calculate the sum of frequencies (∑ f) and the sum of fx (∑ fx). ∑ f = 2+4+10+12+8+4 = 40; ∑ fx = 6+32+130+216+184+112 = 680 Step 3: Apply the formula for the mean of grouped data. Mean (x) = (∑ fx)/(∑ f); x = 680/40; x = 17 b) Construct a cumulative frequency table and use it to determine the median mark. Step 1: Construct the cumulative frequency table, including class boundaries. Marks — f — Class Boundaries — Cumulative Frequency (cf)1-5 — 2 — 0.5 − 5.5 — 2 6-10 — 4 — 5.5 − 10.5 — 2+4=6; 11-15 — 10 — 10.5 − 15.5 — 6+10=16; 16-20 — 12 — 15.5 − 20.5 — 16+12=28; 21-25 — 8 — 20.5 − 25.5 — 28+8=36; 26-30 — 4 — 25.5 − 30.5 — 36+4=40 Step 2: Determine the median position and identify the median class. Total frequency N = 40. The median position is N/2 = 40/2 = 20^(th) value. The cumulative frequency first exceeds 20 in the class 16-20 (cf = 28). So, the median class is 16-20. Step 3: Identify the values for the median formula. The median formula for grouped data is: Median = L + ((N/2 − cf_b)/(f_m)) × w Where: L = Lower class boundary of the median class = 15.5; N = Total frequency = 40; cf_b = Cumulative frequency of the class before the median class = 16; f_m = Frequency of the median class = 12; w = Class width = 5.5 − 0.5 = 5 Step 4: Apply the median formula. Median = 15.5 + ((40/2 − 16)/(12)) × 5; Median = 15.5 + ((20 − 16)/(12)) × 5; Median = 15.5 + (4/12) × 5; Median = 15.5 + 1/3 × 5; Median = 15.5 + 5/3; Median = 15.5 + 1.666... Median ≈ 17.17 c) Determine the mode mark. Step 1: Identify the modal class. The modal class is the class with the highest frequency. From the table, the highest frequency is 12, which corresponds to the class interval 16-20. So, the modal class is 16-20. Step 2: Identify the values for the mode formula. The mode formula for grouped data is: Mode = L + ((f_m − f₁)/((f_m − f₁) + (f_m − f₂))) × w Where: L = Lower class boundary of the modal class = 15.5; f_m = Frequency of the modal class = 12; f₁ = Frequency of the class before the modal class (11-15) = 10; f₂ = Frequency of the class after the modal class (21-25) = 8; w = Class width = 5 Step 3: Apply the mode formula. Mode = 15.5 + ((12 − 10)/((12 − 10) + (12 − 8))) × 5; Mode = 15.5 + ((2)/(2 + 4)) × 5; Mode = 15.5 + (2/6) × 5; Mode = 15.5 + 1/3 × 5; Mode = 15.5 + 5/3; Mode = 15.5 + 1.666... Mode ≈ 17.17

Marks	f	Midpoint (x)	fx
1-5	2	$\frac{1+5}{2} = 3$	$2 \times 3 = 6$
6-10	4	$\frac{6+10}{2} = 8$	$4 \times 8 = 32$
11-15	10	$\frac{11+15}{2} = 13$	$10 \times 13 = 130$
16-20	12	$\frac{16+20}{2} = 18$	$12 \times 18 = 216$
21-25	8	$\frac{21+25}{2} = 23$	$8 \times 23 = 184$
26-30	4	$\frac{26+30}{2} = 28$	$4 \times 28 = 112$

Calculate the number of years, months and days from 1st Jan 2015 to 23rd July 2023, with 365 days to a year and 30 days to a month.

Answers

Step-by-step solution

Part a· 3 steps

Determine the midpoint ( $x$ ) for each class interval and calculate $fx$ .

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

Apply the formula for the mean of grouped data.

Part b· 4 steps
$\textbf{17.17}$

Construct the cumulative frequency table, including class boundaries.

Determine the median position and identify the median class.

Identify the values for the median formula.

Apply the median formula.

Part c· 3 steps
$\textbf{17.17}$

Identify the modal class.

Identify the values for the mode formula.

Apply the mode formula.

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