10 Questions
What is Dillon's GPA/GWA for the given semester?
2.5
In a Statistics Quiz Bee, the ages of five contestants are: 18, 17, 18, 19, and 18. What is their average age?
18
When seven mothers had a blood pressure check, the recorded values were: 415, 398, 402, 400, 420, 415, 407, and 425. What is the median blood pressure?
415
Ten physics students had exam scores of: 23, 45, 50, 23, 26, 28, 40, 23, 40, and 40. What is the mode of their scores?
40 (Unimodal)
What type of data distribution is observed when analyzing the scores of the ten physics students in their exam?
Unimodal
Based on the recorded ages of the five contestants in a Statistics Quiz Bee (18, 17, 18, 19, and 18), which contestant is the oldest?
19 years old
What is the weighted mean of the following values: $3 imes 4 + 4 imes 3 + 1 imes 3 + (2 imes 4)$?
$14$
If Dillon's GPA for a particular semester was rounded to the nearest whole number, what would it be?
$2$
Among the given recorded blood pressure values (415, 398, 402, 400, 420, 415, 407, and 425), which value is closest to the median?
$407$
'14' was calculated as the weighted mean based on some values. Which two values were multiplied by $4$ to get this result?
$3$ and $1$
Study Notes
Statistics
- Statistics is a collection of methods for planning experiments, obtaining data, and then analyzing, interpreting, and drawing conclusions based on the data.
Classification of Variables
- Quantitative variables can be classified as:
- Levels of measurement:
- Nominal
- Ordinal
- Interval
- Ratio
- Levels of measurement:
Measures of Central Tendency
Mean
- The mean is a measure of central tendency that represents the average value of a dataset.
- Example: Find the mean of six friends' test scores: 92, 84, 65, 76, 88, and 90.
- σx = (92 + 84 + 65 + 76 + 88 + 90) / 6 = 82.5
Median
- The median is the middle value in a dataset when it is arranged in order.
- Example: Find the median of seven mothers' blood pressure readings: 135, 121, 119, 116, 130, 121, 131.
- Arrange data in order: 116, 119, 121, 121, 130, 131, 135
- Median = 121
Mode
- The mode is the value that appears most frequently in a dataset.
- Example: Find the mode of the given data set: 15, 28, 25, 48, 22, 43, 39, 44, 43, 49, 34, 22, 33, 27, 25, 22, and 30.
- Arrange data in ascending order: 15, 22, 22, 22, 25, 25, 27, 28, 30, 33, 34, 39, 43, 43, 44, 48, 49
- Mode = 22 (unimodal)
- Example: Find the mode of the given data set: 2, 5, 8, 9, 11, 4, 7, 23.
- No mode exists in this dataset.
- Example: Find the mode of the given data set: 121, 110, 120, 119, 112, 121, 118, 115, 107, 115.
- Arrange data in ascending order: 107, 110, 112, 115, 115, 118, 119, 120, 121, 121
- Mode = 115 and 121 (bimodal)
Weighted Mean
- The weighted mean is the average value of a dataset where each value has a corresponding weight or importance.
- Formula: σ(x ∙ w) / σw
- Example: Find the grade point average of Dillon's semester course grades:
- English (B) = 3 units, History (A) = 4 units, Chemistry (D) = 3 units, Algebra (C) = 4 units
- σ(x ∙ w) = (4 ∙ 3 + 3 ∙ 4 + 1 ∙ 3 + 2 ∙ 4) / (3 + 4 + 3 + 4) = 35 / 14 = 2.5
Test your knowledge on basic concepts in statistics including classification of variables such as quantitative variables and levels of measurement. Explore different methods of sampling used in statistical analysis.
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