Identify the principal amount, interest rate, and time.

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Q(c)

Identify the principal amount, interest rate, and time.
Assuming the loan amount is the cash price of the camera from Q3.b, which is shs. 30,000.
Principal ( $P$ ) = shs. 30,000
Rate ( $R$ ) = 18% p.a. = 0.18
Time ( $T$ ) = 2 years
Calculate the total amount after 2 years using the compound interest formula $A = P(1 + R)^T$ .
$A = \text{shs. } 30,000 (1 + 0.18)^2$ $A = \text{shs. } 30,000 (1.18)^2$ $A = \text{shs. } 30,000 \times 1.3924$ $A = \text{shs. } 41,772$
Calculate the total interest paid.
$\text{Interest} = A - P$ $\text{Interest} = \text{shs. } 41,772 - \text{shs. } 30,000$ $\text{Interest} = \text{shs. } 11,772$
The total interest paid by Kangara is shs. 11,772.
$\boxed{\text{shs. } 11,772}$
Q4. a)
Identify the class with the highest frequency.
From the table, the highest frequency is 30.
State the corresponding class interval.
The class interval corresponding to the frequency of 30 is 40-44 cm.
The modal class is 40-44 cm.
$\boxed{\text{40-44 cm}}$
Q4. b) i)
Create a table to calculate midpoints ( $x$ ) and $fx$ .
Height (cm) Frequency (f) Midpoint (x) fx
20-24 2 22 44
25-29 15 27 405
30-34 18 32 576
35-39 25 37 925
40-44 30 42 1260
45-49 6 47 282
50-54 3 52 156
55-59 2 57 114
Total $\sum f = 101$ $\sum fx = 3762$
Calculate the mean height using the formula $\bar{x} = \frac{\sum fx}{\sum f}$ .
$\bar{x} = \frac{3762}{101}$ $\bar{x} \approx 37.2475$
Rounded to two decimal places, the mean height is 37.25 cm.
$\boxed{37.25 \text{ cm}}$
Q4. b) ii)
Calculate the mean height (already done in Q4.
b) i)).
Mean height = 37.25 cm.

Determine the median class.

Total frequency ( $N$ ) = 101.
The position of the median is $\frac{N}{2} = \frac{101}{2} = 50.5$ .
Create a cumulative frequency (CF) column:

Height (cm)	Frequency (f)	Cumulative Frequency (CF)
20-24	2	2
25-29	15	17
30-34	18	35
35-39	25	60	<-- Median class (CF > 50.5)
40-44	30	90
45-49	6	96
50-54	3	99
55-59	2	101
The median class is 35-39 cm because its cumulative frequency (60) is the first to exceed 50.5.

Identify the values for the median formula.
Lower boundary of the median class ( $L$ ) = 34.5 cm (since the classes are 30-34 and 35-39, the boundary is $(34+35)/2$ ).
Cumulative frequency before the median class ( $CF_b$ ) = 35.
Frequency of the median class ( $f_m$ ) = 25.
Class width ( $w$ ) = $39.5 - 34.5 = 5$ cm.
Calculate the median height using the formula $Median = L + \left(\frac{\frac{N}{2} - CF_b}{f_m}\right) \times w$ .
$Median = 34.5 + \left(\frac{50.5 - 35}{25}\right) \times 5$ $Median = 34.5 + \left(\frac{15.5}{25}\right) \times 5$ $Median = 34.5 + 0.62 \times 5$ $Median = 34.5 + 3.1$ $Median = 37.6 \text{ cm}$
Calculate the difference between the mean height and the median height.
$\text{Difference} = |\text{Mean height} - \text{Median height}|$ $\text{Difference} = |37.25 \text{ cm} - 37.6 \text{ cm}|$ $\text{Difference} = |-0.35 \text{ cm}|$ $\text{Difference} = 0.35 \text{ cm}$
The difference between the mean height and the median height is 0.35 cm.
$\boxed{0.35 \text{ cm}}$

Identify the principal amount, interest rate, and time.

Step-by-step solution

Identify the principal amount, interest rate, and time.

Calculate the total amount after 2 years using the compound interest formula $A = P(1 + R)^T$ .

Calculate the total interest paid.

Identify the class with the highest frequency.

State the corresponding class interval.

Create a table to calculate midpoints ( $x$ ) and $fx$ .

Calculate the mean height using the formula $\bar{x} = \frac{\sum fx}{\sum f}$ .

Calculate the mean height (already done in Q4.

Determine the median class.

Identify the values for the median formula.

Calculate the median height using the formula $Median = L + \left(\frac{\frac{N}{2} - CF_b}{f_m}\right) \times w$ .

Calculate the difference between the mean height and the median height.

Still stuck on this one?

More Economics Questions

Height (cm)	Frequency (f)	Midpoint (x)	fx
20-24	2	22	44
25-29	15	27	405
30-34	18	32	576
35-39	25	37	925
40-44	30	42	1260
45-49	6	47	282
50-54	3	52	156
55-59	2	57	114
Total	$\sum f = 101$		$\sum fx = 3762$

Identify the principal amount, interest rate, and time.

Step-by-step solution

Identify the principal amount, interest rate, and time.

Calculate the total amount after 2 years using the compound interest formula A=P(1+R)TA = P(1 + R)^TA=P(1+R)T.

Calculate the total interest paid.

Identify the class with the highest frequency.

State the corresponding class interval.

Create a table to calculate midpoints (xxx) and fxfxfx.

Calculate the mean height using the formula xˉ=∑fx∑f\bar{x} = \frac{\sum fx}{\sum f}xˉ=∑f∑fx​.

Calculate the mean height (already done in Q4.

Determine the median class.

Identify the values for the median formula.

Calculate the median height using the formula Median=L+(N2−CFbfm)×wMedian = L + \left(\frac{\frac{N}{2} - CF_b}{f_m}\right) \times wMedian=L+(fm​2N​−CFb​​)×w.

Calculate the difference between the mean height and the median height.

Still stuck on this one?

More Economics Questions

Calculate the total amount after 2 years using the compound interest formula $A = P(1 + R)^T$ .

Create a table to calculate midpoints ( $x$ ) and $fx$ .

Calculate the mean height using the formula $\bar{x} = \frac{\sum fx}{\sum f}$ .

Calculate the median height using the formula $Median = L + \left(\frac{\frac{N}{2} - CF_b}{f_m}\right) \times w$ .