- Which of the following is not a measure of central tendency? a. median b. mean c. range d. mode
A. Multiple Choice. Choose the letter of the best answer.
1. Which of the following is not a measure of central tendency? a. median b. mean c. range d. mode ____2. The mean of a set of observations is their __ divided by the number of observations.
a. difference b. sum c. product d. division
3. _________ enables us to calculate an average that takes into account the importance of each value,
to the overall total.
a. arithmetic mean b. weighted mean c. mode d. median
4. _________ of a distribution is/are the value of the variable that divides it into two equal parts.
a. quartile b. percentiles c. median d. deciles
5. After data are arranged in an ordered sequence, _____ divide/divides it into four equal parts.
a. median b. deciles c. percentiles d. quartiles
6. In a data series, when values of the observations are arranged in an ordered sequence, ___
divide/divides the data in ten equal parts.
a. quartiles b. percentiles c. deciles d. median
7. ____ divide/divides the data in one hundred equal parts.
a. median b. percentiles c. quartiles d. deciles
_____8. Suppose that to make the golf team you need to score no more than 73 on average over 5 games. If you
scored 75, 75, 75, and 66 in your first 4 games what is the highest score you can shoot in your 5th game and still
make the team?
a. 75 b. 74 c. 72 d. 76
_____9. The front row in a movie theatre has 23 seats. If you were asked to sit in the seat that occupied the median
position, in which seat would you have to sit?
a. 1 b. 11 c. 23 d. 12
_____10. Which of the following measures can have more than one value for a set of data?
a. median b. mode c. mean d. none of these
B. Solve the following and show your complete solution.
- A petrol station owner records the number of cars which visit his premises on 10 days. The numbers are: 204, 310,
279, 314, 257, 302, 232, 261, 308, 217
a. Find the mean number of cars per day.
b. The owner hopes that the mean will increase if he includes the number of cars on the next day. If 252 cars use the
petrol station on the next day, will the mean increase or decrease?2. The weights, in grams, of seven sweet potatoes are 260, 225, 205, 240, 232, 205, 214. What is the median weight? - In a singing contest, the scores awarded by eight judges were: 5.9 6.7 6.8 6.5 6.7 8.2 6.1 6.3, using the
eight scores, determine:
a. the mean
b. the median
c. the mode
d. Only six scores are to be used. Which two scores may be omitted to leave the value of the median the same? List
all the possible scores. - You are managing a store at the mall and have recorded the value of the average sale for each of 10 randomly
selected days in the last quarter. The data are:
28 32 19 28 29 29 30 32 31 35
19 28 28 29 29 30 31 32 32 35
Find the following:
a. P23
b. P88
c. D4
d. D9
e. Q3
The Correct Answer and Explanation is :
A. Multiple Choice
- Which of the following is not a measure of central tendency?
- c. range The range is a measure of dispersion, not central tendency. Central tendency refers to the mean, median, and mode, which represent the central point of a data set.
- The mean of a set of observations is their __ divided by the number of observations.
- b. sum The mean is calculated by dividing the sum of all observations by the number of observations.
- ___ enables us to calculate an average that takes into account the importance of each value, to the overall total.
- b. weighted mean The weighted mean takes into account the weight or importance of each value in the dataset.
- ___ of a distribution is/are the value of the variable that divides it into two equal parts.
- c. median The median divides a data set into two equal halves when arranged in order.
- After data are arranged in an ordered sequence, __ divide/divides it into four equal parts.
- d. quartiles Quartiles divide the data into four equal parts after sorting the data.
- In a data series, when values of the observations are arranged in an ordered sequence, __ divide/divides the data in ten equal parts.
- c. deciles Deciles divide a data set into ten equal parts.
- _ divide/divides the data in one hundred equal parts.
- b. percentiles Percentiles divide the data into 100 equal parts.
- Suppose that to make the golf team you need to score no more than 73 on average over 5 games. If you scored 75, 75, 75, and 66 in your first 4 games what is the highest score you can shoot in your 5th game and still make the team?
- b. 74 To find the highest possible score on the 5th game, the total sum of the scores must be no more than 73 * 5 = 365. Adding the first four scores gives 75 + 75 + 75 + 66 = 291. Therefore, the highest possible score on the 5th game is 365 – 291 = 74.
- The front row in a movie theatre has 23 seats. If you were asked to sit in the seat that occupied the median position, in which seat would you have to sit?
- b. 12 The median position is the middle value in an odd number of ordered values, so the median position is the 12th seat.
- Which of the following measures can have more than one value for a set of data?
- b. mode The mode can have more than one value if multiple values appear most frequently in a data set, making it bimodal or multimodal.
B. Solutions
1. Petrol Station Owner’s Data
a. Mean number of cars per day:
The numbers of cars are: 204, 310, 279, 314, 257, 302, 232, 261, 308, 217.
To find the mean:
[
\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{204 + 310 + 279 + 314 + 257 + 302 + 232 + 261 + 308 + 217}{10}
]
[
\text{Mean} = \frac{2,674}{10} = 267.4
]
So, the mean number of cars per day is 267.4.
b. Will the mean increase or decrease if 252 cars are added?
The sum of the original data is 2674, and the number of days is 10. With the additional 252 cars, the new sum becomes:
[
2674 + 252 = 2926
]
The new number of days is 11. The new mean is:
[
\text{New Mean} = \frac{2926}{11} = 266.0
]
Since 266.0 is less than 267.4, the mean will decrease.
2. Sweet Potatoes’ Weights (Median Calculation)
The weights in grams are: 260, 225, 205, 240, 232, 205, 214.
Arrange the weights in increasing order: 205, 205, 214, 225, 232, 240, 260.
The median is the middle value of the ordered data. There are 7 values, so the 4th value is the median:
[
\text{Median} = 225 \, \text{grams}
]
3. Singing Contest Scores
Scores: 5.9, 6.7, 6.8, 6.5, 6.7, 8.2, 6.1, 6.3.
a. Mean:
[
\text{Mean} = \frac{5.9 + 6.7 + 6.8 + 6.5 + 6.7 + 8.2 + 6.1 + 6.3}{8} = \frac{54.2}{8} = 6.775
]
b. Median:
Arrange the scores: 5.9, 6.1, 6.3, 6.5, 6.7, 6.7, 6.8, 8.2. The middle two values are 6.5 and 6.7.
[
\text{Median} = \frac{6.5 + 6.7}{2} = 6.6
]
c. Mode:
The mode is the most frequent value. Here, 6.7 appears twice, so:
[
\text{Mode} = 6.7
]
d. Removing two scores without changing the median:
Removing 5.9 and 8.2 would still leave 6.5 and 6.7 as the middle values. Thus, removing 5.9 and 8.2 keeps the median at 6.6.
4. Store’s Daily Sales Data
Data: 28, 32, 19, 28, 29, 29, 30, 32, 31, 35, 19, 28, 28, 29, 29, 30, 31, 32, 32, 35.
a. P23:
The 23rd percentile is the value that separates the lowest 23% of the data. Sort the data and find the 5th value:
[
\text{P23} = 28
]
b. P88:
The 88th percentile is the value that separates the lowest 88% of the data. Sort the data and find the 18th value:
[
\text{P88} = 35
]
c. D4:
The 4th decile corresponds to the 40th percentile, or the 8th value in the sorted list:
[
\text{D4} = 29
]
d. D9:
The 9th decile corresponds to the 90th percentile, or the 18th value in the sorted list:
[
\text{D9} = 35
]
e. Q3:
The third quartile (Q3) corresponds to the 75th percentile, or the 15th value in the sorted list:
[
\text{Q3} = 32
]
These measures help summarize the data effectively, showing central tendencies and variations like percentiles and quartiles.