Statistics & Research Methods
Scales, Central Tendency, Variance & Normal Distribution
PSYC 213 — Statistics for the Behavioural Sciences
Questions & Verified Answers
, Statistics & Research Methods — PSYC 213
25 questions covering scales of measurement, frequency distributions, central tendency, variance, z-
scores, and research methodology.
Q1. What are the four scales of measurement? Give a real example for each.
Answer: Nominal: categories with no order (e.g., types of transport — car, bus, bike).
Ordinal: categories with order but unequal intervals (e.g., restaurant rankings: 1st, 2nd, 3rd).
Interval: equal intervals but no true zero (e.g., temperature in Celsius). Ratio: equal intervals
with a true zero (e.g., weight in kg).
Nominal: classification only.
Ordinal: classification + order.
Interval: classification + order + equal intervals.
Ratio: all of the above + true zero point.
Q2. What is the key difference between interval and ratio scales?
Answer: A ratio scale has a true zero point (zero means complete absence of the quantity),
while an interval scale does not. Only ratio scales allow meaningful multiplication and
division.
Interval example: 0°C does not mean 'no temperature'. You cannot say 40°C is twice as hot as
20°C.
Ratio example: 0 kg means no weight. 10 kg is twice as heavy as 5 kg.
Q3. Using the frequency table (Day: 1-7, Freq: 6,12,8,7,15,4,2), calculate the Mean.
Answer: Mean = 3.61 messages per day
N = 6+12+8+7+15+4+2 = 54
ΣX = (1×6)+(2×12)+(3×8)+(4×7)+(5×15)+(6×4)+(7×2) = 6+24+24+28+75+24+14 = 195
Mean = ≈ 3.61
Q4. Using the same frequency table, calculate the Median.
Answer: Median = 4 messages per day
N=54, so median position = (54+1)/2 = 27.5 → average of 27th and 28th values.
Cumulative frequencies: Day1=6, Day2=18, Day3=26, Day4=33.
The 27th and 28th values both fall in the Day 4 group → Median = 4.
Q5. Using the same frequency table, find the Mode.
Answer: Mode = 5 messages per day
The Mode is the value with the highest frequency.
Day 5 has frequency 15 — the highest in the table.
Q6. Which measure of central tendency best represents the text message data (Mean=3.61,
Median=4, Mode=5)? Why?
Answer: The Median best represents this data.
The distribution is slightly right-skewed (Mode > Median > Mean).
The median is resistant to skewness and is not pulled by extreme values.
The mean is pulled toward the higher values by the high frequency at Day 5.
Rule: use median for skewed data; use mean for symmetric distributions without outliers.
Q7. Calculate the variance for the text message data (Mean=3.61, N=54). Use n-1. Why n-1?
Scales, Central Tendency, Variance & Normal Distribution
PSYC 213 — Statistics for the Behavioural Sciences
Questions & Verified Answers
, Statistics & Research Methods — PSYC 213
25 questions covering scales of measurement, frequency distributions, central tendency, variance, z-
scores, and research methodology.
Q1. What are the four scales of measurement? Give a real example for each.
Answer: Nominal: categories with no order (e.g., types of transport — car, bus, bike).
Ordinal: categories with order but unequal intervals (e.g., restaurant rankings: 1st, 2nd, 3rd).
Interval: equal intervals but no true zero (e.g., temperature in Celsius). Ratio: equal intervals
with a true zero (e.g., weight in kg).
Nominal: classification only.
Ordinal: classification + order.
Interval: classification + order + equal intervals.
Ratio: all of the above + true zero point.
Q2. What is the key difference between interval and ratio scales?
Answer: A ratio scale has a true zero point (zero means complete absence of the quantity),
while an interval scale does not. Only ratio scales allow meaningful multiplication and
division.
Interval example: 0°C does not mean 'no temperature'. You cannot say 40°C is twice as hot as
20°C.
Ratio example: 0 kg means no weight. 10 kg is twice as heavy as 5 kg.
Q3. Using the frequency table (Day: 1-7, Freq: 6,12,8,7,15,4,2), calculate the Mean.
Answer: Mean = 3.61 messages per day
N = 6+12+8+7+15+4+2 = 54
ΣX = (1×6)+(2×12)+(3×8)+(4×7)+(5×15)+(6×4)+(7×2) = 6+24+24+28+75+24+14 = 195
Mean = ≈ 3.61
Q4. Using the same frequency table, calculate the Median.
Answer: Median = 4 messages per day
N=54, so median position = (54+1)/2 = 27.5 → average of 27th and 28th values.
Cumulative frequencies: Day1=6, Day2=18, Day3=26, Day4=33.
The 27th and 28th values both fall in the Day 4 group → Median = 4.
Q5. Using the same frequency table, find the Mode.
Answer: Mode = 5 messages per day
The Mode is the value with the highest frequency.
Day 5 has frequency 15 — the highest in the table.
Q6. Which measure of central tendency best represents the text message data (Mean=3.61,
Median=4, Mode=5)? Why?
Answer: The Median best represents this data.
The distribution is slightly right-skewed (Mode > Median > Mean).
The median is resistant to skewness and is not pulled by extreme values.
The mean is pulled toward the higher values by the high frequency at Day 5.
Rule: use median for skewed data; use mean for symmetric distributions without outliers.
Q7. Calculate the variance for the text message data (Mean=3.61, N=54). Use n-1. Why n-1?
