Question

below are the marks of a test plotted in a back - to - back stem - and - leaf plot
who performed better? explain with justification
key
6 | 7 = 67
find the mean of both:
girls:
boys:
find the mode of both:
girls:
boys:
find the median of both:
girls:
boys:
find the range of both:
girls:
boys:
who has the greater median?

Explanation:

Step1: List out the data

Girls' marks: \(54,57,57,59,60,63,65,66,71,72,74,80,85,89,89,96\)
Boys' marks: \(50,55,56,59,62,65,67,68,72,73,75,79,79,83,84,84,85,91,92\)

Step2: Calculate the mean

• Girls:

$$
LATEXBLOCK0
$$

• Boys:

$$
LATEXBLOCK1
$$

Step3: Find the mode

• Girls: The mode is \(57\) and \(89\) (both appear twice)
• Boys: The mode is \(79\) and \(84\) (both appear twice)

Step4: Calculate the median

• Girls (\(n = 16\), even):

$$
LATEXBLOCK2
$$

• Boys (\(n=19\), odd):

$$ \text{Median}=\text{10th term}=73 $$

Step5: Calculate the range

• Girls: \(\text{Range}=96 - 54=42\)
• Boys: \(\text{Range}=92 - 50 = 42\)

Answer:

• Mean:
• Girls: \(71.0625\)
• Boys: \(\approx72.26\)
• Mode:
• Girls: \(57\) and \(89\)
• Boys: \(79\) and \(84\)
• Median:
• Girls: \(68.5\)
• Boys: \(73\)
• Range:
• Girls: \(42\)
• Boys: \(42\)
• Who has the greater median: Boys
• Who performed better: Boys. Justification: Boys have a higher mean (\(\approx72.26\) vs \(71.0625\)) and a higher median (\(73\) vs \(68.5\))