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What percentage of scores fall below 7 if the nmean is 8 and standard deviation 2?
Assuming a normal distribution, the proportion falling between the mean (of 8) and 7 with standard deviation 2 is:
z = (7 - 8) / 2 = -0.5 → 0.1915 (from normal distribution tables)
→ less than 7 is 0.5 - 0.1915 = 0.3085 = 0.3085 x 100 % = 30.85 %
(Note: the 0.5 in the second sum is because half (0.5) of a normal distribution is less than the mean, not because 7 is half a standard deviation away from the mean, and the tables give the proportion of the normal distribution between the mean and the number of standard deviations from the mean.)
What else can I help you with?
When to you use a z-scores or t-scores?
T score is usually used when the sample size is below 30 and/or when the population standard deviation is unknown.
What is the standard deviation of the data set given below?
A single number, such as 478912, always has a standard deviation of 0.
Compare and contrast the functions of z-scores t-scores and percentile ranks?
Z-scores, t-scores, and percentile ranks are all statistical tools used to understand and interpret data distributions. Z-scores indicate how many standard deviations a data point is from the mean, allowing for comparison across different datasets. T-scores, similar in function to z-scores, are often used in smaller sample sizes and have a mean of 50 and a standard deviation of 10, facilitating easier interpretation. Percentile ranks, on the other hand, express the relative standing of a score within a distribution, showing the percentage of scores that fall below a particular value, thus providing a different type of comparison.
How many SD below or above the mean would this child's z-score of -2 be?
2 standard deviation's below the mean
What does it mean if the standard deviation is greater than the mean?
The standard deviation and the arithmetic mean measure two different characteristics of a set of data. The standard deviation measures how spread out the data is, whereas the arithmetic mean measures where the data is centered. Because of this, there is no particular relation that must be satisfied because the standard deviation is greater than the mean.Actually, there IS a relationship between the mean and standard deviation. A high (large) standard deviation indicates a wide range of scores = a great deal of variance. Generally speaking, the greater the range of scores, the less representative the mean becomes (if we are using "mean" to indicate "normal"). For example, consider the following example:10 students are given a test that is worth 100 points. Only 1 student gets a 100, 2 students receive a zero, and the remaining 7 students get a score of 50.(Arithmetic mean) = 100 + 0(2) + 7(50) = 100 + 0 + 350 = 450/10 studentsSCORE = 45In statistics, the median refers to the value at the 50% percentile. That means that half of the scores fall below the median & the other half are above the median. Using the example above, the scores are: 0, 0, 50, 50, (50, 50), 50, 50, 50, 100. The median is the score that has the same number of occurrences above it and below it. For an odd number of scores, there is exactly one in the middle, and that would be the median. Using this example, we have an even number of scores, so the "middle 2" scores are averaged for the median value. These "middle" scores are bracketed by parenthesis in the list, and in this case are both equal to 50 (which average to 50, so the median is 50). In this case, the standard deviation of these scores is 26.9, which indicates a fairly wide "spread" of the numbers. For a "normal" distribution, most of the scores should center around the same value (in this case 50, which is also known as the "mode" - or the score that occurs most frequently) & as you move towards the extremes (very high or very low values), there should be fewer scores.
When to you use a z-scores or t-scores?
T score is usually used when the sample size is below 30 and/or when the population standard deviation is unknown.
What percentage of the area falls below the mean?
The area between the mean and 1 standard deviation above or below the mean is about 0.3413 or 34.13%
If a normally distributed group of test scores have a mean of 70 and a standard deviation of 12 find the percentage of scores that will fall below 50?
X = 50 => Z = (50 - 70)/12 = -20/12 = -1.33 So prob(X < 50) = Prob(Z < -1.33...) = 0.091
What is the standard deviation of the data set given below?
A single number, such as 478912, always has a standard deviation of 0.
How can you convert standard deviation into percentage?
There must be a formula, but in the mean time there is a handy site that does it for you. [See related link below for the converter]
How do you find the standard deviation for data?
Standard deviation calculation is somewhat difficult.Please refer to the site below for more info
What is he standard deviation of the data set given below 478912?
A single number, such as 478912, always has a standard deviation of 0.
Scores on an exam are normally distributed with a mean of 76 and a standard deviation of 10 In a group of 230 tests how many students score below 66?
There are approximately 16.4% of students who score below 66 on the exam.
If the scores for a test have a mean of 70 and a standard deviation of 12 what percentage of scores will fall below 50?
z=-20/12 = -1.667 Assuming normal distribution, P(Z < -1.667) = 0.04779 or 4.8% of the scores should be less than 50. You can get the probabilities by looking them up on a table or use Excel, where +Normdist(50,70,12,true). My normal table has only 2 digit accuracy so for -1.67 = 0.0475.
Can the Variance ever be smaller than standard deviation?
Yes. If the variance is less than 1, the standard deviation will be greater that the variance. For example, if the variance is 0.5, the standard deviation is sqrt(0.5) or 0.707.
What does a z score of 1.33 mean?
Suppose the random variable, X, that you are studying, has a mean = m, and standard deviation (sd) = s. Then z = 1.33 is equivalent to saying that(x - m)/s = 1.33 or that your observed value is greater than the mean by 1.33 times the sd.
What percentage of data values of a normal distribution will fall within one standard deviation below the mean?
34.1% of the data values fall between (mean-1sd) and the mean.
