For a particular sample of 50 scores on a psychology exam, the following results were obtained.
Mean = 78 Midrange = 72 Third quartile = 94 Mode = 84
Median = 80 Standard deviation = 11 Range = 52 First quartile=68
What score was earned by more students than any other score? Why?
How many students scored between 68 and 94 on the exam?
What was the highest score earned on the exam?
What was the lowest score earned on the exam?
The mode is the most popular grade = 84
68 is the median of the first half
so 25 were between 68 and the median
another 25 were between the median and 94
so
50 students between first quartile 68 and third quartile 94
Mid range is 72.
That is half way between lowest and highest. Range = 52 so high = 72 +52/2 and low = 72 -52/2
so
low = 46
high = 98
To determine the score that was earned by more students than any other score, we need to find the mode of the sample. The mode is the value that appears most frequently in the dataset.
To find the mode, we look at the given information: Mode = 84. Therefore, the score that was earned by more students than any other score is 84.
Now let's find out how many students scored between 68 and 94 on the exam. We can do this by looking at the first and third quartiles. The first quartile (Q1) represents the 25th percentile and the third quartile (Q3) represents the 75th percentile.
From the given information, the first quartile (Q1) is 68 and the third quartile (Q3) is 94. This means that 25% of the scores are below 68 and 75% of the scores are below 94. To find the number of students who scored between 68 and 94, we subtract the percentage below 68 from the percentage below 94.
75% - 25% = 50%. Therefore, 50% of the students scored between 68 and 94 on the exam.
Next, let's determine the highest and lowest scores earned on the exam. The range is the difference between the highest and lowest score, so we can use the given range value.
From the given information, the range is 52. The range is calculated by subtracting the lowest score from the highest score. So, to find the highest score, we add the range to the lowest score.
Lowest score + Range = Highest score
Lowest score + 52 = Highest score
Using the information provided, we don't have the specific value of the lowest score, so we can't determine the exact highest score earned on the exam. We only know that the range is 52.
To summarize:
- The score earned by more students than any other score is 84 (the mode).
- 50% of the students scored between 68 and 94 on the exam.
- The highest score earned on the exam cannot be determined with the given information.
- The lowest score earned on the exam cannot be determined with the given information.