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Math Chapter 11 : Topic 2
Averages in Real Life
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A company distributes bonuses of Rs. $10,000$, $15,000$, $20,000$, and $25,000$ to four employees. The mean bonus is:
Reasoning: Mean $=$ $\frac{(10000\ + \ 15000\ + \ 20000\ + \ 25000)}{4} = \frac{70000}{4} = 17,500$
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In a survey, a city records populations (in thousands): $50$, $60$, $70$, $80$, $90$. The median population is:
Reasoning: Middle value in ordered data $= 70$
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A shop sells items with prices: $50$, $60$, $50$, $70$, $50$, $80$. The mode is:
Reasoning: Most frequent value $= 50$
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A government allocates funds: Education $(40\%)$, Health $(30\%)$, Defense $(30\%)$. If total budget$\ \ \ = \ 100$ billion, weighted mean allocation per sector is:
Reasoning: Weighted mean $=$ total / number of sectors $= 100/3 \approx 33.3$
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Marks of students are: $10$, $20$, $30$, $40$. If weights are $1$, $2$, $3$, $4$ respectively, weighted mean is:
Reasoning: Weighted mean $=$ $\frac{10\ \times \ 1\ + \ 20\ \times \ 2\ + \ 30\ \times \ 3\ + \ 40\ \times \ 4}{1\ + \ 2\ + \ 3\ + \ 4}$$=$ $\frac{10\ + \ 40\ + \ 90\ + \ 160}{10} = \frac{300}{10} = 30$
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If median income of a population increases, it indicates:
Reasoning: Median represents the middle value
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A dataset has mean$\ = 50$. If a new value $100$ is added, the mean will:
Reasoning: Adding a value greater than mean increases average
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In marketing, the most sold product is determined using:
Reasoning: Mode gives most frequent value
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For even number of observations, median is:
Reasoning: Median $=$ average of two central values
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A project has costs: $100$, $200$, $300$ with weights $2$, $3$, $5$. Weighted mean cost is:
Reasoning: $\frac{100\ \times \ 2\ + \ 200\ \times \ 3\ + \ 300\ \times \ 5}{2\ \ + \ 3\ + \ 5} = \frac{200\ + \ 600\ + \ 1500}{10} = \frac{2300}{10}$ $= 230$
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If all values in a dataset are equal, then:
Reasoning: All measures coincide
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Which measure is least affected by extreme values?
Reasoning: Median ignores outliers
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Daily sales (units): $5$, $7$, $7$, $9$, $10$. Mode is:
Reasoning: Most frequent value $= 7$
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If weights are equal, weighted mean becomes:
Reasoning: Weighted mean reduces to simple mean
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Which measure is best for income distribution analysis?
Reasoning: Median avoids distortion by extreme incomes
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A dataset: $2$, $4$, $6$, $8$, $100\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightarrow \ \ $ mean is misleading because:
Reasoning: Outlier $(100)$ skews mean
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In forecasting population growth, which measure is commonly used?
Reasoning: Mean gives overall trend
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If frequency of value increases, it affects:
Reasoning: Mode changes directly, mean also shifts.
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A teacher gives different weights to assignments and exams. This is an example of:
Reasoning: Different importance $\Longrightarrow$ weights
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Median of $3$, $5$, $7$, $9$, $11$, $13$ is:
Reasoning: Median $= (7 + 9)\ /\ 2 = 8$
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Which measure helps identify the most popular brand?
Reasoning: Mode $=$ most frequent
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If data is highly skewed, best measure is:
Reasoning: Median is resistant to skewness
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Weighted mean is useful when:
Reasoning: Weights represent importance
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Which measure uses all data values?
Reasoning: Mean includes every value
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A dataset has two modes. It is called:
Reasoning: Two most frequent values
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